Privacy-Preserving Federated Learning for Artificial Intelligence Agriculture Disease Detection Under Heterogeneous Farm Data Silos: A Computer Differential-Privacy Utility Evaluation

Federated learning allows agricultural disease-detection models to be trained across farms without centralising raw imagery, but the differential-privacy noise added to protect each farm's updates degrades the very accuracy that motivates the collaboration. the present analysis formalises that trade-off for heterogeneous farm data silos and evaluates it computationally. A federated averaging protocol with per-client Gaussian mechanism is specified, and a utility model is derived that separates the privacy budget, the number of participating silos and the heterogeneity of local label distributions into distinct terms. The model is then evaluated in a replication-based computational study: 2000 replications per design cell across cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points, under a declared variance structure with between-cluster SD 6.0, residual SD 4.5 and intraclass correlation 0.64. The contribution is a design-theoretic account of when differential-privacy noise in federated agricultural learning remains compatible with disease-detection accuracy, and a specification of the cluster counts and privacy budgets under which that compatibility holds.